EXACT BOUNDARY OBSERVABILITY AND CONTROLLABILITY OF THE WAVE EQUATION IN AN INTERVAL WITH TWO MOVING ENDPOINTS

被引：8

作者：

Sengouga, Abdelmouhcene ^{[1
]}

机构：

[1] Univ Msila, Fac Math & Comp Sci, Lab Funct Anal & Geometry Spaces, Msila 28000, Algeria

来源：

EVOLUTION EQUATIONS AND CONTROL THEORY | 2020年 / 9卷 / 01期

关键词：

Wave equation; noncylindrical domains; generalised Fourier series; observability; controllability; Hilbert uniqueness method; STABILIZATION; DOMAINS; PART;

D O I：

10.3934/eect.2020014

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the wave equation in an interval with two linearly moving endpoints. We give the exact solution by a series formula, then we show that the energy of the solution decays at the rate 1/t. We also establish observability results, at one or at both endpoints, in a sharp time. Moreover, using the Hilbert uniqueness method, we derive exact boundary controllability results.

引用

页码：1 / 25

页数：25

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